This is a single-center, open-label study in adult renal transplant patients. Fifteen patients will receive TLI, ATG, and an infusion of CD34+ selected G-CSF mobilized blood cells combined with a fixed number (1x10^6) of CD3+ T cells from the same mobilized blood cell source. Patients will receive a one-month course of mycophenolate mofetil and a six to 12 month tapering course of cyclosporine that will be discontinued at six months. At serial timepoints (1) graft function will be monitored, (2) chimerism will be measured in recipient white blood cell subsets, (3) mixed lymphocyte response (MLR) assays of peripheral blood mononuclear cells against donor and third party cells will be performed, and (4) protocol biopsies of the graft will be obtained. An attempt will be made to discontinue cyclosporine at six months if (1) chimerism is detectable for at least 180 days after CD34+ and CD3+ cell infusion, (2) there is stable graft function without clinical rejection episodes, and (3) there is lack of histologic rejection on protocol biopsies. In the proposed study, patients will be given a target dose of 8-10x10^6 CD34+ cells/kg and 1x10^6 CD3+ cells/kg because sustained chimerism may be necessary for sustained tolerance to the graft.